Transcript g related measurements: GWL, ADS, Dalitz

Measurement of the CKM angle g
with a D0 Dalitz analysis of the
B±→D(*)K± decays at BaBar
Nicola Neri
INFN Pisa
International School of Subnuclear Physics
Erice, 30 Aug - 6 Sept 2006
CKM matrix and Unitarity Triangle
 Vud Vus Vub 


V   Vcd Vcs Vcb 
V

V
V
ts
tb 
 td

Unitarity of
quark mixing matrix
V V V V V V  0
*
ud ub
CP violation is proportional to the triangle area
 
 VudVub
CP violation  g  arg 
 0, 
 
 VcdVcb 
(r,h)
Vud Vub*
|Vcd Vcb* |
a
g
(0,0)September 1st 2006 Erice
*
cd cb
*
td tb
Standard Model fits predicts g
•(64±5 )˚ UTFit - Bayesian
•(60±5 )CKMFit - Frequentist
Vtd Vtb*
|Vcd Vcb* |
•Test SM prediction
with tree-level processes
b
Nicola Neri - International School of
Subnuclear Physics
(1,0)
2
Towards g
bc transition
bu transition
Vus*
If same final state
 interference
 g measurement
Vcb
f
Vub
Vcs*
f
A(B-D0 K-) = ABrB e i(dB-g)
A(B-D0 K-) = AB
f = KS (Dalitz Analysis)
f = CP
f = DCSD
(GLW)
(ADS)
Critical parameter
rB 
A(b  uc s)
A(b  cu s)
Theoretically and experimentally
difficult to determine.
September 1st 2006 Erice
CKM elements +
color suppression
strong phase
in B decay
Gronau, Wyler, Phys. Lett. B265,172 (1991)
D. Atwood, I. Dunietz, A. Soni
Phys.Rev. D63 (2001) 036005
Nicola Neri - International School of
A. Giri, Y. Grossman, A. Soffer, J. Zupan
Subnuclear Physics
Phys.Rev. D68 (2003) 054018
3
Three-body D decays: Dalitz plot

A point of in a three-body decay phase-space can be determined
with two independent kinematical variables. A possible choice is to
represent the state in the Dalitz plot (s12 , s13 )
kinematical Mandelstam variables:
     , s  p K  p  
s12  p1 K s0  p2  
2
13
1
0
s
 2
3
)2
(MD0-m
(MD0-m)2
The A(D0 →Ks) amplitude can be
written as AD(s12, s13).
(mKS+m2
(mKS+m2
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
4
D0
D0 3-body decay
Dalitz distribution
|AD(s12, s13) |2 (*)
s12 (GeV2)
s12 (GeV2)
Using AD(s12, s13) in B decay amplitude
D0
s13 (GeV2)
s13 (GeV2)
A(B- ) = AD(s12, s13) +rB ei(-g+dB) AD(s13, s12)
CP
A(B+ )
= AD (s13, s12) +rB
ei
(g+dB A ((s , s )
D
12
13
Assuming CP is
conserved in D decays
gfrom the
Interference term
|A(B- )|2 =| AD(s12, s13) |2 + rB2 | AD(s13, s12) |2 +
The method suffers of a two-fold ambiguity
g , d B   g   , d B   
+2rBRe[AD(s12, s13) AD(s13, s12)* ei(-g+dB)]
If rB is large, good precision on g
 
AD(s12, s13): fitted on D*  D0  with D 0  K S0   from e e  cc
2006
(*)September
 Erice
m2 
Def. 1sts12
    
p1 K s0
   p  
Nicola
Neri - International School of
 2
2 Physics
0
p2 
, sSubnuclear
13  m  p1 K s 
 2
3
5
Model Dependent Breit-Wigner
description of 2-body amplitudes



Three-body D0 decays proceed mostly via 2-body decays (1 resonance + 1
particle)
The D0 amplitude AD can be fit to a sum of Breit-Wigner functions plus a
constant term, see E.M. Aitala et. al. Phys. Rev. Lett. 86, 770 (2001)
For systematic error evaluation, use K-Matrix formalism to overcome the
main limitation of the BW model to parameterize large and overlapping Swave resonances.
AD (s12 , s13 )  a0e
Ar (s12 , s13 ) 
id 0


r
ar eid r Ar (s12 , s13 )
M rJ
= angular dependence of the amplitude
 BW
depends on the spin J of the resonance r
1
r
Relativistic Breit-Wigner with
BW ( sij ) 
mass dependent width r
2
sij  M r  imr r ( sij )
J
Mr
r
where sij=[s12,s13,s23] depending on the resonance Ks-,Ks+,+-. mr is the mass of the resonance
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
6
The BaBar Isobar model
K892
390K sig events
BaBar Data with
BaBar isobar model
fit over imposed.
Fit Fraction=1.20
D*  D 0 
D 0  K S0  
97.7% purity
Good fit in DCS K*(892) region.
r770
K DCS
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
7
The BaBar Isobar Model
BaBar model 16 resonances + 1 constant term (Non-resonant).
Mass and widths are fixed to the PDG values.
Except for K*(1430), use E791 values and for s, s`, fit from data.
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
8
Signal events and DATA sample
–
DATA at (4S) peak 10.580 GeV
316.3 fb-1 (347 M BB events)
–
DATA below peak
23.3
e-
(4S) e+
9.1 GeV
(4S)
fb-1
rate = L·s(bb) ~ 1.2·1034cm-2s-1 ·1.1 nb ≳ 13 BB evt/sec
3.0 GeV
B
50% B0B0

X
50% B+B-
(4S)
cosa Ks
B-



p Ks  ( x Ks  x D0 )
  

p Ks x Ks  x D0
B-
D0 KKs
=1 for signal events
+ + -
September 1st 2006 Erice
D*0 K-
B

D0 0 ,D0 g
D
0

K S0
a Ks


K
-

Ks + + Nicola Neri - International School of
Subnuclear Physics
9
Yields on DATA
Signal
D
BB
qq
D0K
347 million of BB pairs at (4S)
D*0K D*0 D0
D*0K D*0 D0g
BD0K
39823 signal events ~60% purity mES>5.272 GeV/c2
BD*0K D*0 D0
9713 signal events
~80% purity
BD*0K D*0 D0g
9312 signal events
~50% purity
q q background is >5 times the B B bkg contribution in each mode. D contribution is negligible after all the
selection criteria applied in signal region unless for [D0]K. The error on the Dcontribution is large and can
be explained as a statistical fluctuation (accounted for in systematic error)
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
10
Dalitz distributions
D*K  (D00)K
DK
B-
B+
B-
B+
D*K  (D0g)K
B-
September 1st 2006 Erice
B+
Dalitz plot distribution for signal events
after all the selection criteria applied.
Nicola Neri - International School of
Subnuclear Physics
11
CP parameters extraction
Fit for different CP parameters: cartesian coordinates are preferred base.
Errors are gaussian and pulls are well behaving.
y= Im[rBexpi(dg)=
x= Re[rBexpi(dg)]= rBcos(dg) ,
rBsin(dg)
CP parameter
x-=rBcos(dg)
y-=rBsin(dg)
x+=rBcos(dg)
y+=rBsin(dg)
Result
CP parameter
x*-=rBcos(dg)
y*-=rBsin(dg)
x*+=rBcos(dg)
y*+=rBsin(dg)
Result
Main systematics
PDF shapes , Dalitz plot efficiency,
qq Dalitz shape
Charge correlation of (D0,K) in qq
Dalitz model error.
Account for phenomenological D
amplitude parameterization uncertainty
The statistical error dominates the measurement.
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
12
Cartesian coordinate results
1s
2s
D0K
D*0K
B-
B+
B+
d
d
B-
Direct CPV
Direct CP violation d=2 rb(*)|sing|
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
13
Experimental systematic errors
Statistical error
September 1st 2006 Erice
>>
Experimental systematics
Nicola Neri - International School of
Subnuclear Physics
≳
Dalitz model systematics
14
Frequentist interpretation of the results
D*0K
D0K
2s
1s
r*B
rB
1s (2s) excursion
s is to be understood in term of 1D proj of a L in 5D.
Nicola Neri - International School of
September 1st 2006 Erice
Stat
Subnuclear Physics
Syst
Dalitz
15
Considerations on the results
Dx≈Dy≈rb·Dq
B-
(
g)
y
s(g) ≈ Dx/rb
rb
Dq
rB
rb
Dq
B+
September 1st 2006 Erice
x
Experimentally we can improve the measurement of the CP
cartesian coordinates but the improvement on error of g
depends on the true value of the rb parameter.
Similar behavior for statistical and systematic error.
Nicola Neri - International School of
Subnuclear Physics
16
Conclusions and perspectives
• We demonstrated that the measurement of g is possible and compatible with SM
predictions.
•Dalitz method gives the best sensitivity to gbut …more statistics is crucial.
•If rB≥0.1 we will know the g value ≤15% precision with 1 ab-1.
Toy MC
rb=0.1 assumed
Dalitz model error projection
g=73±29 ([15,136]@95%CL)
g=-107±29 ([-165,-44]@95%CL)
September 1st 2006 Erice
Near Future
Nicola Neri - International School of
Subnuclear Physics
17
Back-up slides
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
18
Dalitz model systematics

 S-wave:


 P-wave:







Allow K*0(1430) mass and width to be determined from the fit
Use LASS parameterization with LASS parameters
K P-wave:


Zemach Tensor as the Spin Factor for f2(1270) and K*2(1430) BW
K S-wave:


Change r(770) parameters according to PDG
Replace Gounaris-Sakurai by regular BW
 and K D-wave


Use K-matrix  S-wave model instead of the nominal BW model
Use BJ/psi Ks + as control sample for K*(892) parameters
Allow K*(892) mass and width to be determined from the fit
Blatt-Weiskopf penetration factors
Running width: consider a fixed value
Remove K2*(1430), K*(1680), K*(1410), r(1450)
This is a more realistic and detailed estimate of the model systematics !
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
19
Bias on x-, x+ for alternative Dalitz models
Residual for the x-, x+ coordinates wrt the nominal CP fit.
September band
1st 2006 Erice
Yellow
is the nominal fit
Nicola Neri - International School of
Subnuclear
Physics
statistical
error
(x100 Run1-5
statistics)
20
Bias on y-, y+ for alternative Dalitz models
Residual for the y-, y+ coordinates wrt the nominal CP fit.
September band
1st 2006 Erice
Yellow
is the nominal fit
Nicola Neri - International School of
Subnuclear
Physics
statistical
error
(x100 Run1-5
statistics)
21
Background parameterization: Dalitz
shape for background events
●
BB and continuum events are divided in real D0 and fake D0. The real D0 fraction is
evaluated on qq and BB Monte Carlo counting:
●
●
cross-check on DATA using the mES<5.272 GeV sidebands and fitting the D 0 mass.
For the bkg real D0 : D0 Dalitz signal shape
For the bkg fake D0 (combinatorial) 2D symmetric 3rd order polynomial asymmetric
function :
• cross-check on DATA using the mES<5.272 GeV and D0 mass sidebands
.qq combinatorics – MC
fit function
.BB combinatorics - MC
fit function
Asymmetric
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
Asymmetric
22
Background parameterization:
fraction of true D0
●
The real D0 fraction is evaluated directly on DATA using the mES<5.272 GeV
sidebands and fitting the D0 mass distribution. The signal is a Gaussian with
fixed s6MeV/c2 (MC value) and m1864.5MeV/c2 (PDG value).
On Monte Carlo we find the fraction for
true D0 to be:
RCont  0.2218  0.0097 MC continuum evt
RBB  0.0255  0.0076 MC BB events
RBkg  0.1588  0.0062
MC BB + qq weighted evt
. DATA (On-Res)
Rdata  0.254  0.035
we use this error for conservative systematic error evaluation
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
23
Background characterization:
true D0 and flavor-charge correlation
D0=KS
e+
e-
cc
D0
K-
R RS 
+ other particles
# B  D0 K 
# B   D 0 K  # B   D 0 K 
estimated on Monte Carlo events
RS
RCont
 0.164 0.018, RBRSB  0.64  0.15
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
24
Final results
•We have measured the cartesian CP fit parameters for DK (x±,y±) and D*K (x*± ,y*±)
using 316 fb-1 BaBar data:
CP parameter
x-=rBcos(dg)
y-=rBsin(dg)
x+=rBcos(dg)
y+=rBsin(dg)
Statistical error
Result
CP parameter
x*-=rBcos(dg)
y*-=rBsin(dg)
x*+=rBcos(dg)
y*+=rBsin(dg)
Experimental systematics
Result
D0 amplitude model uncertainty
•This measurement supersedes the previous one on 208 fb-1 with significant
improvements in the method and smaller errors on the cartesian CP parameters.
•Using a Frequentist approach we have extracted the values of the CP parameters:
1s (2s) excursion
s is to be understood in term of 1D proj of a L in 5D.
Syst
Nicola Neri -Stat
International School
of
September 1st 2006 Erice
Subnuclear Physics
Dalitz
25
CP Violation in the Standard Model


CP symmetry can be violated in any field theory with at least
one CP-odd phase in the Lagrangian
This condition is satisfied in the Standard Model through the
three-generation Cabibbo-Kobayashi-Maskawa (CKM) quarkmixing matrix
b
u
Vub
September 1st 2006 Erice
c
t
d
s b
Wolfenstein parameterization: corresponds to a
W
Vud
V   Vcd
V
 td
u
Vus
Vcs
Vts
particular choice of the quark-phase convention
1 2

1




2
Vub  
1 2


Vcb  

1 

2
Vtb   3
2
 A (1  r  ih )  A

Nicola Neri - International School of
Subnuclear Physics
CP-violating phase

A 3 ( r  ih ) 

  O ( 4 )
A 2


1


  0.23
26
Unitarity triangle

CP violation is proportional to the area
 
 VudVub
 0, 
CP violation  g  arg 
 
 VcdVcb 
(r,h)
*
Vud Vub
|Vcd Vcb* |
a
g
Vtd Vtb*
|Vcd Vcb* |
b
(1,0)
(0,0)
VudVub*  VcdVcb*  VtdVtb*  0
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
27
CP violation in decay or
direct CP violation
A f |H |B
A
A
2
f
B
A f |H|B

2
f
B

CP violation
For example A=A1+A2: two amplitudes with
a relative CP violating phase g (CP-odd) and
a CP conserving phase d (CP-even)
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
28
BaBar Detector
1.5T solenoid
DIRC PID)
144 quartz bars
11000 PMs
EMC
6580 CsI(Tl) crystals
e+ (3.1GeV)
Drift Chamber
40 stereo layers
e (9.0 GeV)
Silicon Vertex Tracker
5 layers, double-sided sensors
Instrumented Flux Return
iron / RPCs/LSTs (muon / neutral hadrons)
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
29
Dalitz: BaBar vs Belle Results HFAG
Experiment
Belle‘06
N(BB)=392M
BABAR'06
N(BB)=347M
Mode
γ/φ3 (°)
DK–
D→KSπ+π–
53± +15–18 ± 3 ± 9
D*K–
D*→Dπ0
D→KSπ+π–
53 ± +15–18 ± 3 ± 9
δB (°)
146 ± 19 ± 3 ± 23
302 ± 35 ± 6 ± 23
DK–
D→KSπ+π–
92 ± 41 ± 10 ± 13
118 ±64 ±21 ±28
D*K–
D*→D(π0,γ)
D→KSπ+π–
92 ± 41 ± 10 ± 13
298 ±59 ±16 ±13
rB
0.16 ± 0.05 ± 0.01 ± 0.05
0.18 +0.11–0.10 ± 0.01 ± 0.05
<0.142
<0.206
BaBar measurement is very important since it stresses one more time
the difficulty to measure gin a regime where the uncertainty on rb is quite large.
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
30
BaBar vs Belle experimental results
BABAR'06 - N(BB)=347M
CP parameter
Result
CP parameter
Result
x*-=rBcos(dg)
y*-=rBsin(dg)
x*+=rBcos(dg)
y*+=rBsin(dg)
x-=rBcos(dg)
y-=rBsin(dg)
x+=rBcos(dg)
y+=rBsin(dg)
Belle’06 - N(BB)=386M
0.03
+0.07
0.17
+0.09
−0.08
± 0.01
−0.12
± 0.02
−0.14 ± 0.07 ± 0.02
−0.09 ± 0.09 ± 0.01
CP parameter
x*-=rBcos(dg)
y*-=rBsin(dg)
x*+=rBcos(dg)
y*+=rBsin(dg)
Result
−0.13
+0.17
−0.34
+0.17
−0.15
−0.16
± 0.02
± 0.03
0.03
± 0.12
± 0.01
0.01
± 0.14
± 0.01
given on rb,g,d
x-=rBcos(dg)
y-=rBsin(dg)
x+=rBcos(dg
y+=rBsin(dg)
Result
given on rb,g,d
CP parameter
Experimental measurement of the CP parameters x,y is more precise wrt Belle even
with slightly smaller statistics. Different error on g is due to Belle larger central values.
Statistical
September error
1st 2006 Erice
Nicola Neri - International School of
Experimental
systematics
Subnuclear
Physics
D0 amplitude model uncertainty
31
Outline







Theoretical framework
D0 decay amplitude parameterization
Selection of the D(*)K events
CP parameters from the D0 Dalitz distribution
Systematic errors
Extraction of g
Conclusions
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
32
Selection criteria for B±D(*)K± decay modes
D0K
D*0K (D0p0)
D*0K (D0g)
|cos T|
<0.8
<0.8
<0.8
|mass(D0)-PDG|
<12MeV
<12MeV
<12MeV
|mass(Ks)-PDG|
<9MeV <9MeV
<9MeV
E g
---->30 MeV
>100MeV
|mass(0)-PDG|
----<15MeV
----Kaon Tight Selector Yes
Yes
Yes
|DM-PDG|
----<2.5MeV
<10.0MeV
cos aKs
>0.99
>0.99
>0.99
|DE |
<30MeV
<30MeV
<30MeV
---------------------------------------------------------------------------------------- efficiency
15%
7%
9%
--------------------------------------------------------------------------------------signal events
398±23
97±13
93±12
cos aKs suppress fake Ks
|cos T| suppress jet-like events
Kaon Tight Selector (LH) and |DE|<30 MeV
September 1st 2006 Erice
suppress D(*)p events
Nicola Neri - International School of
Subnuclear Physics
33
Likelihood for Dalitz CP fit
A(B-) = |AD(s12,s13) +rBei(-gdBAD(s13,s12) |2
|AD(s12,s13)|2
|AD(s13,s12)|2
From MC and D0 sideband data
aD0,D0
fSig,Dh,Cont,BB from data (extended likelihood  yields)
RCont, BB
True D0 fraction from MC and data (mES
sidebands)
# B   D0 K 
RS
RCont,BB,WrongSig 
Charge-flavor correlation from
# B   D0 K   # B   D0 K 
MC
Nicola Neri - International School of
September 1st 2006 Erice
Subnuclear Physics
34
(D0g)K – (D00)K cross-feed






From Monte Carlo simulation the cross-feed between the samples is
due to events of (D00)K where we loose a soft g and we reconstruct
it as a (D0g)K.
Since the cross-feed goes in one direction (D00)K  (D0g)K, it is
correct to assign common events to the (D00)K signal sample.
After all the cuts and after this correction applied we expect <5% of
signal (D0g)K from cross-feed.
A systematic effect to the cross-feed has been assigned adding a
signal component according to the (D00)K Dalitz PDF and
performing the CP fit.
The systematic bias of the fit with and without (D00)K has been
quoted as systematic error.
Negligible wrt the other systematic error sources.
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
35
Dalitz model systematic error:
K*(1430) parameters
Current BaBar model for K*0(1430):
Mass =1.412 +/- 0.006 GeV
Width = 294 +/- 23
MeV
E791 Isobar model for K*0(1430):
Mass =1.459+/-0.007 GeV
Width = 175 +/- 12 MeV
BaBar Isobar model [float] for K*0(1430):
PDG
(from LASS)
Mass =1.495 +/- 0.01 GeV
Width = 183 +/- 9
MeV
The Isobar model, the fit prefer small value of K*(1430),
both seen in E791 and BaBar, although PDG list the width 294 MeV
Mass and width are not unique parameters, depend on the parameterization
and Non-Resonant model
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
36
K*(892) and K*(1430) with new parameters
Perfect!
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
37
Zemach Tensor vs Helicity model
Affects seriously on spin 2
Monte Carlo simulation using f2(1270)
Data Ds
MC
MC
Data
In Dsthe non-resonant term is much smaller (5%) in Zemach Tensor while the
non-resonant term is (25%) if Helicity model is used
 D wave systematics
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
38
Dalitz model systematic error:
K*(892) parameters
 In PDG those measurements are from 1970’s. Very low statistics ~5000 events
we have ~200000 K*(892) events
If we allow mass and width to float, we get the width 46 +/- 0.5 MeV, mass 893 +/- 0.2 MeV
 Partial wave analysis of BJ/psi K  decay
(BaBar) can use as control sample
 Mass=892.9+/-2.5 MeV
 Width=46.6 +/-4.7 MeV
 Their values are consistent with our floated
values
No S-wave!
Very clean measurement
 Consider as systematics compared with PDG
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
39
Procedure for Dalitz model systematics






Generate a high statistics toy MC (x100 data statistics) experiment
using nominal (BW) model.
The experiment is fitted using the nominal and each alternative
model.
Produce experiment-by-experiment differences for all (x,y)
parameters for each alternative Dalitz model.
For each CP coordinates, consider the squared sum of the residuals
over all the alternative models as the systematic error.
Since the model error increases with the value of rb we
conservatively quote a model error corresponding to ~rb+1svalue
that we fit on data.
This is a quite conservative estimate of the systematics and we
believe it is fair to consider the covariance matrix among the CP
parameters to be diagonal.
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
40
CA D0 K*(892)- +
s13 (GeV2)
Sensitivity to g
s 2 (g ) ~
1
d 2 ln( L)
dg 2
points : weight = 1
d 2 ln( L)
weight =
dg 2
DCS D0
K0*(1430)+-
DCS D0 K*(892)+-
D0 Ks r
s12 (GeV2)
Strong phase variation improves the sensitivity to g.
Isobar model formalism reduces discrete ambiguities on the value of g to a two-fold ambiguity.
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
41
Reconstruction of exclusive B±D(*)K± decays
B

X
Y(4S)
e-
e+
cosa Ks



p Ks  ( x Ks  x D0 )
  

p Ks x Ks  x D0
B-
B
K S0
K
B-
a Ks


=1 for signal events
D0 KKs + + -
September 1st 2006 Erice

D
0

-

D*0 KD0 0 ,D0 g
Ks + + -
Nicola Neri - International School of
Subnuclear Physics
42
Background characterization: relative
fraction of signal and bkg samples
Continuum events are the largest bkg in the analysis.
We apply a cut |cos(T)|<0.8 and we use fisher PDF for the continuum bkg
suppression.
Fisher = F [LegendreP0,LegendreP2,|cos T|,|cos B*|]
●
The Fisher PDF helps to evaluate the relative fraction of BB and continuum
events directly from DATA.
●
D0K
D*0K - D*0 D0
D*0K - D*0 D0g
Signal
D
BB
qq
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
43
Efficiency Map for D*→D0p
We use ~200K D* MC sample D0 Phase Space to compute the efficiency map .
2D 3rd order polynomial function used
for the efficiency map.
Purity 97.7%
Red = perfectly flat efficiency
Blu = 3rd order polynomial fit
Efficiency is almost flat
in the Dalitz plot. The fit
without eff map gives Nicola Neri - International School of
Septembersimilar
1st 2006 Erice fit results.
Subnuclear Physics
very
44
Isobar model formalism
As an example a D0 three-body decay D0 ABC decaying through an r=[AB]
resonance
In the amplitude we include
FD, Fr the vertex factors of the
D and the resonance r respectively.
H.Pilkuhn, The interactions of hadrons,
Amsterdam: North-Holland (1967)
AD (s12 , s13 )  a0eid 
0
D0 three-body amplitude

ar eidr Ar (s12 , s13 )
r
can be fitted from DATA using a
 
D0
flavor tagged sample from
e e  cc events selecting D*  D0  with D0  K S0  
•We fit for a0 ,ar amplitude values and the relative phase f0 , fr among resonances,
constant over the Dalitz plot.
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
45
Efficiency Map for B->DK (*)
●
●
Because of the different momentum range we use a different
parametrization respect to the D* sample.
We use ~1M B->D(*)K signal MC sample with Phase Space D0 decay to
compute the efficiency mapping.
Fit for 2D 3rd order polynomial function to parametrize the efficiency
mapping:
 (s12 , s13 )  e0  e1 (s12  s12 )  e2 (s12 2  s132  s12 s13 )  e3 (s123  s133  s12 2 s13  s12 s132 )
Efficiency is rather flat
in the Dalitz plot.
CP Fit without eff map to
quote the systematic error
on CP parameters
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
46
K-Matrix formalism for  S-wave
1. K-Matrix formalism overcomes the main limitation of the BW model to
parameterize large and overlapping S-wave resonances. Avoid the
introduction of not established s,s´ scalar resonances.
†
2. By construction unitarity is satisfied
SS =1 S=1+2iT
T=(1-iK·r)-1K
where S is the scattering operator
T is the transition operator
ris the phase space matrix
K-matrix D0 three-body amplitude
AD (s12 , s13 )  F1 s23  
F1 s23  

r spin 0,k spin 0 
-1






I
i
K
s
ρ
s
23
23 1j P j s 23 

j
September 1st 2006 Erice
ar eidr Ar (s12 , s13 )
F1 =  S-wave amplitude
Pj(s) = initial production vector
Nicola Neri - International School of
Subnuclear Physics
47
The CLEO model
CLEO model 10 resonances + 1 Non Resonant term.
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
48
The CLEO model
With >10x more data than CLEO, we find that the
model with 10 resonances is insufficient to describe the data.
CLEO model 10 resonances +
1 Non Resonant term.
BaBar Data refitted
using CLEO model.
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
49
The BELLE model
Belle model 15 resonances + 1 Non Resonant term.
Added DCS K*0,2(1430), K*(1680) and 1 , 2 respect to the
CLEO Model. With more statistics you “see” a more detailed
structure.
Added
Added
Added
Added
Added
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
50
The BELLE model
DCS region is quite
important for the g
sensitivity. See plot
in the next pages.
BELLE Data with
BELLE model fit
overimposed.
Not very good fit for DCS K*(892) region.
Belle model 15 resonances + 1 Non Resonant term.
Added DCS K*0,2(1430), K*(1680) and
1Neri
, -2International
respect to
theof
Nicola
School
September
1st 2006 Erice
CLEO
Model.
Subnuclear Physics
51
The BaBar Model
BaBar model does not include the DCS K*(1680) and DCS K*(1410)
because the number of events expected is very small.
K*(1680)
DCS K*(1680)
Moreover the K*(1680) and the DCS K*(1680) overlap in the
same Dalitz region: the fit was returning same amplitude for CA
and DCS!
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
52
The BaBar model
2 fit evaluation of goodness of fit:
CLEO model is 2.2/dof(3054)
Belle model is 1.88/dof(1130)
1.27/dof(3054).
Total fit fraction:
CLEO model is 120%
Belle model is 137%
125.0%
The 2 is still not optimal but much better respect to all
Dalitz fit published so far.
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
53
The BaBar K-matrix model
K892
BaBar Data with
BaBar K-matrix model
fit over imposed.
Fit Fraction=1.11
390K sig events
D*  D0 
D 0  K S0  
97.7% purity
opens KK channel
r770
K DCS
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
54
K-Matrix parameterization according
to Anisovich, Sarantev


K ij s23   


gia g aj
 ma  s
2
r

f ijscatt
23




1.0  s0scatt 
 1.0  s A0
2
s

s
m
23
A  /2
scatt 
s23  s0 
 s23  s A0
V.V. Anisovitch, A.V Sarantev Eur. Phys. Jour. A16, 229 (2003)

Adler zero term to accommodate singularities
ga
th
where
i is the coupling constant of the K-matrix pole mato the i channel 1= 2=KK
3=multi-meson 4= hh 5= hh´.
f ijscatt , s0scatt
P j s  
slow varying parameter of the K-matrix element.
ba g aj

a ma  s
2
September 1st 2006 Erice
23
 f1prod
j
1.0  s0scatt
s23  s0scatt
f ijscatt  0 if i  1  
Pj(s) = initial production vector
I.J.R. Aitchison, Nucl. Phys. A189, 417 (1972)
Nicola Neri - International School of
Subnuclear Physics
55
The BaBar K-Matrix Model
BaBar K-Matrix model 9 resonances +  S-wave term. Total fit fraction is 1.11.
 S-wave term
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
56
Overview of Dalitz CP fit strategy
Extract as much as possible information from data
Step 1: selection PDF shapes and yields
Fit as many as possible component yields and discriminating
variables (PDF) shapes from simultaneous fit to DK and Dp
data
Fix the remaining to MC estimates
Selection PDFs: mES, Fisher
●
Step 2: Dalitz CP fit to extract CP parameters from the D0 Dalitz
distribution
Fix shape PDF parameters obtained in step 1 and perform
Dalitz CP fit alone with yields re-floated
Impact of fixing shape PDFs on CP violation parameters
is small (systematic error taken into account)
●
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
57
The frequentist method


Frequentist (classical) method determines a CL regions where the
probability that the region will contain the true point is a.
Determine PDF of fitted parameters as a function of the true
parameters:
 In principle, fitted-true parameter mapping requires multidimensional scan of the experimental (full) likelihood:
 Prohibitive amount of CPU, limited precision (granularity of the
scan).
Make optimal choice of fitted parameters and try analytical
construction for the PDF. Gaussian PDF are easy to integrate!
Cartesian coordinates (x,y)
x= Re[rBexpi(dg)]= rBcos(dg) ,
Im[rBexpi(dg)= rBsin(dg)
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
y=
58
The Frequentist PDF
Single channel (D0K o D*0K)
Measured parameters (4D): z+=(x+, y+), z-=(x-, y-)
Truth parameters (3D): pt=(rB,g, d)
G2(z;x,y,x,y,r) is a 2D Gaussian
with mean (x,y) and sigma (x,y)
Easy to include
systematic error by
replacing stat→ tot
D0K-D*0K combination
Measured parameters (8D): z+, z-, z*+, z*Truth parameters (5D): pt=(rB,g, d, r*B, d*)
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
59
Confidence Regions
CL=1-a(pt)
Integral a Example in 1D
P(data|pt)
Integration domain D
D
Pt .data
.z
a(pt): calculated analytically, PDF is product of gaussians.
●We calculate 3D (5D) joint probability corresponding to 1 and 2
CL
for a 3D (5D) gaussian distribution.
●Make 1D projections to quote 1 and 2 regions for r ,g,d,r *,d*
b
b
●
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
60
Cartesian coordinates: toy MC
Linear correspondence and errors are well behaving.
y-
y+
Fitted parameters vs Generated parameters.
x-
September 1st 2006 Erice
x+
Nicola Neri - International School of
Subnuclear Physics
61
Confidence Regions (CR):
D0K-D*0K combination
CL=1-a(pt)
Integration domain D (CR)
September 1st 2006 Erice
Nicola Neri - International School of
Subnuclear Physics
62
D0K-D*0K confidence intervals
Single channel (D0K o
D*0K)
D0K-D*0K
combination
September 1st 2006 Erice
Central values are the mean of CL the
Nicola Neriinterval
- International School of
Subnuclear Physics
63
BD*K decays help in constraining g
As pointed out in Phys.Rev.D70 091503 (2004) for the BD*K decay we have:
~
*
D*  D*0  rB ei (d *g ) D *0
A( B   D *0 K  )
rB 
*
A( B   D*0 K  )
From the momentum parity conservation in the D* decay:
(*) 0
CP 
D

D
(*) 0
D
D  D 0


*
D D g


CP(π )  1
CP(γ)  1
0
(*) 0
2
Opposite CP
*
eigenstate
The effective  strong phase shift helps in the determination of g

  
BR B  D Dg K   a 1  r


BR B   D * D 0 K   a 1  rB2  2rB cos d  g 

September 1st 2006 Erice
*
2

2
2
B

 2rB cos d  g 
Nicola Neri - International School of
Subnuclear Physics
64